On the existence of atomic models

Details On the existence of atomic models On the existence of atomic models

1993-01-15

arxiv.org/abs/math/9301210v1

J. Symbolic Logic 58 (1993), 1189--1194

Mathematics

Logic

Scientific paper

We give an example of a countable theory T such that for every cardinal
lambda >= aleph_2 there is a fully indiscernible set A of power lambda such
that the principal types are dense over A, yet there is no atomic model of T
over A. In particular, T(A) is a theory of size lambda where the principal
types are dense, yet T(A) has no atomic model.

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